Synodic Cycle
A synodic cycle refers to a periodic pattern in the orbit of two heavenly bodies, which is marked by their transit from being aligned (conjunct) to being anti-aligned (opposite) and back and forth. The synodic cycle of the Sun and Moon is the most well-studied cycle of our solar system and is known as the Moon Cycle. New moons correspond to the Sun-Moon conjunction, while full moons correspond to the Sun-Moon opposition. Explanation Understanding synodic cycles is possible through understanding an analog clock. Each hand of a clock has a certain rotational period. The second hand takes T=60 seconds to complete one cycle, while the minute hand takes T=60 minutes to complete one cycle and the hour hand takes T=12 hours to complete one cycle. This defines the period of each of the hands, but a 'synodic period' can only be defined relative to some pair of 'hands'. Second-Minute Assuming it is 12:00:00 PM, all three hands are aligned at the 12. A second-minute synod is the cycle between this time and the next time in which the second hand aligns parallel to the minute hand (opposite directions = anti-parallel). At 12:01:00 PM the second hand has returned to 12 (T=60 seconds has passed), but now the minute hand has moved forward by a 1/60th of its path. Hence, it is not until about 12:01:01 PM that the second hand aligns with the minute hand and hence the second-minute synod has a period of about T = 61.02 seconds. Minute-Hour Similarly, if we take the path from 12:00:00 PM to 1:00:00 PM, then in this 60 minutes, the minute hand has returned to its original position, but now the hour hand has moved by 1/12th of its path. Even now, if we wait another 5 minutes (60/12) the minute hand will now align with the previous position of the hour hand, but now the hour hand has moved another 1/144th of its path (1/12th as far as before). Waiting another 1/12th of 5 minutes (25 seconds) will approach ever so slightly closer, and then another ~2 seconds (25/12) and so on. Roughly speaking the minute hand will align with the hour hand after: 1 hour + 5 minutes + 25 seconds + 25/12 seconds + 25/144 seconds + ... = 1 hour, 5 minutes and 29.34 seconds. Second-Hour Lastly, a second-hour synod is quite similar to a second-minute synod, only the hour hand moves even more slowly, and hence the extra time to traverse the path only leaves the second-hour synod at: 60 seconds + 60/(12*60) + 60/(12*60)^2 + ... = 60.083 seconds Examples For planetary synods, each planet acts like one of the hands on the clock, all rotating with their own periods around the sun. The key difference, is that from a geocentric point of view, these orbits are not circular and can even appear retrograde, hence synodic periods are defined as the average of many cycles, since each cycle will be different depending on the Earth's position. Jupiter-North Node ) and the red line represents the orbital phase of the North Node. Crossings indicate points where both are in the same direction (but doesn't take geocentric frame into account)]] Jupiter's orbital period is 11.86 years, while the North Node's period is 18.6 years. Saturn - Pluto: http://mauricefernandez.com/the-saturn-pluto-conjunction-and-the-transits-for-the-year-2020/ Category:Synodic Cycle Category:Astrology Category:Outer Planets